Transcript Powerpoint Slides for the Standard Version of Starting Out

Standard Version of
Starting Out with C++, 4th
Edition
Chapter 8
Searching and Sorting Arrays
Copyright 2003
Scott/Jones Publishing
Topics
8.1 Introduction to Search Algorithms
8.3 Introduction to Sorting Algorithms
8.5 Sorting and Searching Vectors
Chapter 8 slide 2
8.1 Introduction to Search
Algorithms
• Search: locate an item in a list of
information
• Two algorithms (methods):
– Linear search
– Binary search
Chapter 8 slide 3
Linear Search
• Algorithm:
set found to false; set position to –1; set index to 0
while index < number of elts. and found is false
if list[index] is equal to search value
found = true
position = index
end if
add 1 to index
end while
return position
Chapter 8 slide 4
Linear Search - Example
• Array numlist contains:
17
23
5
11
2
29
3
• Searching for the the value 11, linear
search examines 17, 23, 5, and 11
• Searching for the the value 7, linear
search examines 17, 23, 5, 11,
2, 29, and 3
Chapter 8 slide 5
Linear Search - Tradeoffs
• Benefits:
– Easy algorithm to understand
– Array can be in any order
• Disadvantages:
– Inefficient (slow): for array of N elements,
examines N/2 elements on average for
value in array, N elements for value not in
array
Chapter 8 slide 6
Binary Search
Requires array elements to be in order
1. Divides the array into three sections:
–
–
–
middle element
elements on one side of the middle element
elements on the other side of the middle element
2. If the middle element is the correct value, done.
Otherwise, go to step 1. using only the half of
the array that may contain the correct value.
3. Continue steps 1. and 2. until either the value is
found or there are no more elements to
examine
Chapter 8 slide 7
Binary Search - Example
• Array numlist2 contains:
2
3
5
11
17
23
29
• Searching for the the value 11, binary
search examines 11 and stops
• Searching for the the value 7, linear
search examines 11, 3, 5, and stops
Chapter 8 slide 8
Binary Search - Tradeoffs
• Benefits:
– Much more efficient than linear search.
For array of N elements, performs at most
log2N comparisons
• Disadvantages:
– Requires that array elements be sorted
Chapter 8 slide 9
8.3 Introduction to Sorting
Algorithms
• Sort: arrange values into an order:
– Alphabetical
– Ascending numeric
– Descending numeric
• Two algorithms considered here:
– Bubble sort
– Selection sort
Chapter 8 slide 10
Bubble Sort
Concept:
– Compare 1st two elements
• If out of order, exchange them to put in order
– Move down one element, compare 2nd and 3rd
elements, exchange if necessary. Continue
until end of array.
– Pass through array again, exchanging as
necessary
– Repeat until pass made with no exchanges
Chapter 8 slide 11
Bubble Sort - Example
Array numlist3 contains:
17
23
5
11
compare values
17 and 23 – in correct
order, so no exchange
compare values 23 and
5 – not in correct order,
so exchange them
Chapter 8 slide 12
compare values 23 and
11 – not in correct order,
so exchange them
Bubble Sort – Example (2)
After first pass, array numlist3 contains:
17
5
11
23
compare values 17 and
5 – not in correct order,
so exchange them
compare values 17 and
11 – not in correct order,
so exchange them
Chapter 8 slide 13
compare values 17 and
23 – in correct order,
so no exchange
Bubble Sort – Example (3)
After second pass, array numlist3 contains:
5
11
17
23
compare values 5 and
11 – in correct order,
so no exchange
compare values 11 and
17 – in correct order,
so no exchange
Chapter 8 slide 14
compare values 17 and
23 – in correct order,
so no exchange
No exchanges, so
array is in order
Bubble Sort - Tradeoffs
• Benefit:
– Easy to understand and implement
• Disadvantage:
– Inefficient: slow for large arrays
Chapter 8 slide 15
Selection Sort
• Concept for sort in ascending order:
– Locate smallest element in array.
Exchange it with element in position 0
– Locate next smallest element in array.
Exchange it with element in position 1.
– Continue until all elements are arranged in
order
Chapter 8 slide 16
Selection Sort - Example
Array numlist contains:
11
2
29
3
1. Smallest element is 2. Exchange 2
with element in 1st position in array:
2
Chapter 8 slide 17
11
29
3
Selection Sort – Example (2)
2. Next smallest element is 3. Exchange
3 with element in 2nd position in array:
2
3
29
11
3. Next smallest element is 11. Exchange
11 with element in 3rd position in array:
2
Chapter 8 slide 18
3
11
29
Selection Sort - Tradeoffs
• Benefit:
– More efficient than Bubble Sort, since
fewer exchanges
• Disadvantage:
– May not be as easy as Bubble Sort to
understand
Chapter 8 slide 19
8.5 Sorting and Searching
Vectors
• Sorting and searching algorithms can
be applied to vectors as well as arrays
• Need slight modifications to functions to
use vector arguments:
– vector <type> & used in prototype
– No need to indicate vector size – functions
can use size member function to
calculate
Chapter 8 slide 20
Standard Version of
Starting Out with C++, 4th
Edition
Chapter 8
Searching and Sorting Arrays
Copyright 2003
Scott/Jones Publishing